Abstract
This paper discusses algorithms for measuring indirect control in complex corporate shareholding networks and investigates the importance of mutual connections in the network in the sense of shareholdings of one firm in another. Our algorithms rely on the concept of power indices from cooperative game theory. We focus on a variant of the implicit power index by Stach and Mercik based on the absolute Banzhaf index. We extend this algorithm by determining the number of regressions in an adaptive network-dependent manner taking into account the maximal length of a path to each controlled company in the network and by a model for the float, i.e., the set of unidentified small shareholders. We compare our method with existing algorithms and discuss the importance of linkages by investigating divestment of shares for a theoretical network with 21 players.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Algaba, E., Bilbao, J., Fernández, J., Jiménez, N., López, J.: Algorithms for computing the Myerson value by dividends. In: Moore, K.B. (ed.) Discrete Mathematics Research Progress, pp. 1–13. Nova Science Publishers (2007)
Algaba, E., Bilbao, J.M., Fernández Garcıa, J.R.: The distribution of power in the European constitution. Eur. J. Oper. Res. 176(3), 1752–1766 (2007). https://doi.org/10.1016/j.ejor.2005.12.002
Algaba, E., Bilbao, J.M., Fernández Garcıa, J.R., López, J.: Computing power indices in weighted multiple majority games. Math. Soc. Sci. 46(1), 63–80 (2003). https://doi.org/10.1016/S0165-4896(02)00086-0
Algaba, E., Fragnelli, V., Sánchez-Soriano, J.: Handbook of the Shapley value. CRC Press, Boca Raton (2020). https://doi.org/10.1201/9781351241410
Alonso-Meijide, J.M., Bowles, C., Holler, M.J., Napel, S.: Monotonicity of power in games with a priori unions. Theor. Decis. 66(1), 17–37 (2009). https://doi.org/10.1007/s11238-008-9114-2
Bang-Jensen, J., Gutin, G.Z.: Digraphs: theory, algorithms and applications. Springer Science & Business Media, Berlin (2008)
Banzhaf, J.F.: Weighted voting doesn’t work: a mathematical analysis. Rutgers L. Rev. 19, 317–343 (1965)
Berghammer, R., Bolus, S.: On the use of binary decision diagrams for solving problems on simple games. Eur. J. Oper. Res. 222(3), 529–541 (2012)
Berghammer, R., Bolus, S., Rusinowska, A., De Swart, H.: A relation-algebraic approach to simple games. Eur. J. Oper. Res. 210(1), 68–80 (2011)
Bertini, C., Freixas, J., Gambarelli, G., Stach, I.: Comparing power indices. Int. Game Theory Rev. 15(02), 1340004 (2013)
Bertini, C., Mercik, J., Stach, I.: Indirect control and power. Oper. Res. Decisions 26(2), 7–30 (2016). https://doi.org/10.5277/ord160202
Bertini, C., Stach, I.: Banzhaf voting power measure. In: Dowding, K. (ed.) Encyclopedia of Power, SAGE Publications, pp. 54–55. Sage Publications (2011)
Bolus, S.: Power indices of simple games and vector-weighted majority games by means of binary decision diagrams. Eur. J. Oper. Res. 210(2), 258–272 (2011)
Bolus, S.: A QOBDD-based approach to simple games. Ph.D. thesis, Christian-Albrechts Universität Kiel (2012)
Borm, P., Owen, G., Tijs, S.: On the position value for communication situations. SIAM J. Discret. Math. 5(3), 305–320 (1992)
Chakravarty, S.R., Mitra, M., Sarkar, P.: A Course on Cooperative Game Theory. Cambridge University Press, Cambridge (2015)
Crama, Y., Leruth, L.: Control and voting power in corporate networks: concepts and computational aspects. Eur. J. Oper. Res. 178(3), 879–893 (2007). https://doi.org/10.1016/j.ejor.2006.02.020
Crama, Y., Leruth, L.: Power indices and the measurement of control in corporate structures. Int. Game Theory Rev. 15(03), 1340017 (2013). https://doi.org/10.1142/S0219198913400173
Csardi, G., Nepusz, T., et al.: The igraph software package for complex network research. Int. J. complex syst. 1695(5), 1–9 (2006). https://igraph.org/
Deegan, J., Packel, E.: A new index of power for simple n-person games. Int. J. Game Theory 7(2), 113–123 (1978)
Derks, J., Haller, H.: Null players out? linear values for games with variable supports. Int. Game Theory Rev. 1(03n04), 301–314 (1999)
Dubey, P., Shapley, L.S.: Mathematical properties of the Banzhaf power index. Math. Oper. Res. 4(2), 99–131 (1979)
Eddelbuettel, D., et al.: RCPP: seamless R and C++ integration. J. Stat. Softw. 40(8), 1–18 (2011)
Fernández, J.R., Algaba, E., Bilbao, J.M., Jiménez, A., Jiménez, N., López, J.J.: Generating functions for computing the Myerson value. Ann. Oper. Res. 109(1), 143–158 (2002). https://doi.org/10.1023/A:1016348001805
Holler, M.J.: Forming coalitions and measuring voting power. Polit. Stud. 30(2), 262–271 (1982)
Holler, M.J., Packel, E.: Power, luck and the right index. Z. f. Nationalökonomie 43(1), 21–29 (1983). https://doi.org/10.1007/BF01283881
Johnston, R.: On the measurement of power: some reactions to Laver. Environ. Plan. A 10(8), 907–914 (1978). https://doi.org/10.1068/a100907
Karos, D., Peters, H.: Indirect control and power in mutual control structures. Games Econom. Behav. 92, 150–165 (2015). https://doi.org/10.1016/j.geb.2015.06.003
Kirsch, W., Langner, J.: Power indices and minimal winning coalitions. Soc. Choice Welf. 34(1), 33–46 (2010). https://doi.org/10.1007/s00355-009-0387-3
Lange, F., Kóczy, L.Á.: Power indices expressed in terms of minimal winning coalitions. Soc. Choice Welf. 41(2), 281–292 (2013). https://doi.org/10.1007/s00355-012-0685-z
Leech, D.: Voting power in the governance of the international monetary fund. Ann. Oper. Res. 109(1), 375–397 (2002). https://doi.org/10.1023/A:1016324824094
Leech, D.: Computing power indices for large voting games. Manage. Sci. 49(6), 831–837 (2003)
Leech, D.: Power indices in large voting bodies. Public Choice 155(1), 61–79 (2013)
Levy, M.: Control in pyramidal structures. Corp. Gov. Int. Rev. 17(1), 77–89 (2009)
Levy, M.: The Banzhaf index in complete and incomplete shareholding structures: a new algorithm. Eur. J. Oper. Res. 215(2), 411–421 (2011)
Levy, M., Szafarz, A.: Cross-ownership: a device for management entrenchment? Rev. Finan. 21(4), 1675–1699 (2017). https://doi.org/10.1093/rof/rfw009
Malawski, M.: Counting power indices for games with a priori unions. In: Gambarelli, G. (ed.) Essays in Cooperative Games. Theory and Decision Library, vol. 36, pp. 125–140. Springer, Boston (2004). https://doi.org/10.1007/978-1-4020-2936-3_10
Matsui, Y., Matsui, T.: NP-completeness for calculating power indices of weighted majority games. Theoret. Comput. Sci. 263(1–2), 305–310 (2001)
Mercik, J., Gładysz, B., Stach, I., Staudacher, J.: Shapley-based estimation of company value-concept, algorithms and parameters. Entropy 23(12), 1598 (2021). https://doi.org/10.3390/e23121598
Mercik, J., Łobos, K.: Index of implicit power as a measure of reciprocal ownership. In: Nguyen, N.T., Kowalczyk, R., Mercik, J. (eds.) Transactions on Computational Collective Intelligence XXIII. LNCS, vol. 9760, pp. 128–140. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52886-0_8
Mercik, J., Ramsey, D.M.: The effect of Brexit on the balance of power in the European union council: an approach based on pre-coalitions. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 87–107. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70647-4_7
Mercik, J., Stach, I.: On measurement of control in corporate structures. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds.) Transactions on Computational Collective Intelligence XXXI. LNCS, vol. 11290, pp. 64–79. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-58464-4_7
Myerson, R.B.: Graphs and cooperation in games. Math. Oper. Res. 2(3), 225–229 (1977)
Shapley, L.S.: A value for n-person games. In: Kuhn, H., Tucker, A. (eds.) Contributions to the Theory of Games II, pp. 307–317. Princeton University Press (1953). https://doi.org/10.1515/9781400881970-018
Shapley, L.S., Shubik, M.: A method for evaluating the distribution of power in a committee system. Am. Polit. Sci. Rev. 48(3), 787–792 (1954). https://doi.org/10.2307/1951053
Stach, I.: Shapley-Shubik index. In: Dowding, K. (eds.) Encyclopedia of Power, pp. 603–606. Sage Publications (2011)
Stach, I.: Indirect control of corporations: analysis and simulations. Decis. Mak. Manuf. Serv. 11(1–2), 31–51 (2017). https://doi.org/10.7494/dmms.2017.11.1-2.31
Stach, I.: Sub-coalitional approach to values. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 74–86. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70647-4_6
Stach, I., Mercik, J.: Measurement of control power in corporate networks. Oper. Res. Decis. 31(1), 97–121 (2021). https://doi.org/10.37190/ord210106
Stach, I., Mercik, J., Bertini, C.: Some propositions of approaches for measuring indirect control power of firms and mutual connections in corporate shareholding structures. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds.) Transactions on Computational Collective Intelligence XXXV. LNCS, vol. 12330, pp. 116–132. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-662-62245-2_8
Staudacher, J.: Computing the public good index for weighted voting games with precoalitions using dynamic programming. In: Power & Responsibility: Interdisciplinary Perspectives for the 21st Century in Honor of Manfred J. Holler, p. 17. Springer, Berlin (2022)
Staudacher, J., Anwander, J.: Using the R package CoopGame for the analysis, solution and visualization of cooperative games with transferable utility, R Vignette (2021). https://cran.r-project.org/package=CoopGame
Staudacher, J., et al.: Computing power indices for weighted voting games via dynamic programming. Oper. Res. Decis. 31(2), 123–145 (2021). https://doi.org/10.37190/ord210206
Staudacher, J., Olsson, L., Stach, I.: Implicit power indices for measuring indirect control in corporate structures. In: Nguyen, N.T., Kowalczyk, R., Motylska-Kuźma, A., Mercik, J. (eds.) Transactions on Computational Collective Intelligence XXXVI. LNCS, vol. 13010, pp. 73–93. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-64563-5_4
Staudacher, J., Wagner, F., Filipp, J.: Dynamic programming for computing power indices for weighted voting games with Precoalitions. Games 13(1), 6 (2022). https://doi.org/10.3390/g13010006
The R Core team and others: R: A language and environment for statistical computing. Vienna, Austria (2021). https://www.r-project.org/
Wickham, H.: R packages: organize, test, document, and share your code. O’Reilly Media (2015). https://r-pkgs.org/
Acknowledgements
The first author thanks the funding of the Bavarian State Ministry of Science and Arts. The third author’s contribution to the article was funded under subvention funds for the AGH University of Science and Technology in Krakow, Poland. The authors thank two anonymous reviewers for their careful reading of the manuscript and their helpful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Ethics declarations
Conflict of Interest
The authors declare no conflicts of interest.
Rights and permissions
Copyright information
© 2022 Springer-Verlag GmbH Germany, part of Springer Nature
About this chapter
Cite this chapter
Staudacher, J., Olsson, L., Stach, I. (2022). Algorithms for Measuring Indirect Control in Corporate Networks and Effects of Divestment. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXVII. Lecture Notes in Computer Science(), vol 13750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66597-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-66597-8_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-66596-1
Online ISBN: 978-3-662-66597-8
eBook Packages: Computer ScienceComputer Science (R0)